Question

lesson 8: how many solutions?
cool down: how does she know?
elena began to solve this equation:
\\(\frac{12x + 6(4x + 3)}{3} = 2(6x + 4) - 2\\)
\\(12x + 6(4x + 3) = 3(2(6x + 4) - 2)\\)
\\(12x + 6(4x + 3) = 6(6x + 4) - 6\\)
\\(12x + 24x + 18 = 36x + 24 - 6\\)
when she got to the last line she stopped and said the equation is true for all values of \\(x\\).
how could elena tell?

Explanation:

Answer:

Simplifying both sides results in \(36x + 18 = 36x + 18\), which is an identity, so it is true for all values of \(x\).